A comparative study of different machine learning methods for dissipative quantum dynamics

TL;DR

This study compares 22 machine learning models, including neural networks and kernel methods, for predicting long-time dissipative quantum dynamics from short-time data, highlighting the efficiency of kernel ridge regression and convolutional recurrent models.

Contribution

It benchmarks various ML models for quantum dynamics prediction, identifying effective and computationally inexpensive methods like nonlinear KRR and convolutional GRUs.

Findings

Kernel ridge regression with nonlinear kernels is accurate and inexpensive.

Convolutional Gated Recurrent Units outperform other neural network models.

Nonlinear KRR is suitable for cases with fixed input trajectory lengths.

Abstract

It has been recently shown that supervised machine learning (ML) algorithms can accurately and efficiently predict the long-time populations dynamics of dissipative quantum systems given only short-time population dynamics. In the present article we benchmaked 22 ML models on their ability to predict long-time dynamics of a two-level quantum system linearly coupled to harmonic bath. The models include uni- and bidirectional recurrent, convolutional, and fully-connected feed-forward artificial neural networks (ANNs) and kernel ridge regression (KRR) with linear and most commonly used nonlinear kernels. Our results suggest that KRR with nonlinear kernels can serve as inexpensive yet accurate way to simulate long-time dynamics in cases where the constant length of input trajectories is appropriate. Convolutional Gated Recurrent Unit model is found to be the most efficient ANN model.